Pricing Longevity Risk - Richards Consulting

Pricing Longevity Risk - Richards Consulting

Modelling Annuitant Mortality: UK v. France Hlne Queau and Stephen Richards Copyright UMR and Stephen Richards Consulting Ltd Overview 1. 2. 3. 4. 5. 6.

Regional variation in France. Modelling regional mortality with UMR data. Socio-economic group in UK. Annuitant longevity in UK. Does UK-style analysis work for UMR data? Conclusions and questions. 1. Regional variation in France Region Figures are

period life expectancies in 2007. Rhne-Alpes Midi-Pyrnes Poitou-Charentes le-de-France Pays de la Loire Corse Aquitaine Centre

Provence-Alpes-Cte d'Azur Languedoc-Roussillon Limousin Franche-Comt Bourgogne Basse-Normandie Alsace Auvergne Bretagne Haute-Normandie Champagne-Ardenne Lorraine

Picardie Nord-Pas-de-Calais Female life expectancy Difference 85.2 85.0 85.0 84.9 84.9 84.8 84.7 84.6

84.6 84.5 84.5 84.4 84.3 84.2 84.0 83.9 83.8 83.6 83.5 83.1

82.4 82.2 0.3 0.1 0.1 0.0 0.0 -0.1 -0.2 -0.3 -0.3

-0.4 -0.4 -0.5 -0.6 -0.7 -0.9 -1.0 -1.1 -1.3 -1.4 -1.8 -2.5

-2.7 Sources : Insee, tat-civil (donnes domicilies), estimations localises de population. 1. Regional variation in France Do UMR annuitants have these same differentials? The answer lies in building a statistical model and fitting it to some experience

data 2. Modelling mortality Mortality model Survival model for force of mortality, x.

16 models considered (Richards, 2010). Best-fitting model is Makeham-Perks: , and are estimated from the data. 2. UMR portfolio data

Mainly educational professionals. 130,468 records of anuitants over age 60. 582,922 life-years of exposure. 8,949 deaths. 99.2% of annuitants have French address. 2. Region

24 regions, including overseas territories and foreign addresses. le-de-France has most annuitants, so treat this as the baseline to measure against. On average one department will appear significantly different just by chance: (241)*5%=1.15. 2. Region as risk factor in UMR Source: UMR and Longevitas Ltd. le-de-France is the baseline and the parameter for this is implicitly zero. Other parameters such as Age, Gender and Time are not shown for reasons of space.

2. Regional variation in UMR data 1 region has significantly lighter mortality: Provence-Alpes-Cte d'Azur. 3 regions have significantly heavier mortality: Lorraine, Pays de la Loire, and Picardie.

4 significant differences v. 1.15 expected. 2. Regional variation Results for Lorraine and Picardie match population data. Can we do better than using region? What about using socio-economic group?

3. Socio-economic group 3. Socio-economic group in UK Socio-economic status determined by occupation. Significant variation in life expectancy Source: ONS data from longitudinal study on population data.

3. Socio-economic group Socio-economic status determined by occupation. Occupation often not available or reliable. Question: How to include in annuity pricing? Answer: Use variables which are correlated with socioeconomic group or replace it.

3. Socio-economic group Two possible replacements: 1. Pension size, i.e. indicator of wealth and income. 2. Geodemographic type, i.e. a direct profile of lifestyle based on location. 3. Geodemographic profile

Grouping of people with shared characteristics. Based on address or postcode using information about the people who live there (housing type, car ownership etc) In the UK this is based on postcode 3. Structure of a UK postcode

3. Postcodes Each postcode covers 1517 households 1.7 million postcodes in UK Too many to use directly! Use geodemographic type

Example: Mosaic from Experian 3. Mosaic classification 4. Annuitant mortality in UK 4. Annuitant mortality in UK Richards & Jones (2004) found several risk factors:

Age Gender Pension size Postcode Duration since retirement Region

Source: Richards and Jones (2004) using life-company annuitant mortality experience. Importance of socio-economic group Factor Step change Reserve change Gender

Femalemale -11.5% Lifestyle Topbottom -11.4% Duration

Shortlong -10.8% Income Highlow -5.9% Region

SouthNorth -5.9% Source: Richards and Jones (2004) Financial aspects of longevity risk, SIAS, p39 4. Annuitant mortality in UK Postcodes have been confirmed as risk factors in other works: Richards (2008) and

Madrigal et al (2009). 5. Does this apply to UMR data? 5. UMR log(mortality) by age Source: UMR and Longevitas Ltd 5. log(mortality) by age and gender Source: UMR and Longevitas Ltd

5. UMR mortality by pension size Source: UMR and Longevitas Ltd. Crude mortality rate per decile with 1 being smallest 10% of pensions and 10 being the 10% with the largest pensions. 5. Risk factors for UMR annuitants As in the UK, the following are risk factors: 1. Age 2. Gender 3. Pension size

But not geodemographic type! 5. Geodemographics in France Geodemographic type based on lot.

An lot covers around 90 households in Paris but can cover an entire town or village in rural areas (commune). A UK postcode covers 1517 households. 5. Geodemographics and UMR data

54 geodemographic types. Expect two or three to appear significant by chance: (54-1)*5%=2.65. F25 has largest exposure time, so make this the baseline. Only two geodemographic types have significantly different mortality. 5. Why is geodemographic type not significant here?

Some possibilities: 1. UK postcode has finer granularity than French lot. 2. UMR portfolio is homogeneous with respect to occupation: educational professionals. 3. France is more egalitarian than the UK. 6. Conclusions and questions 1. Pension size a significant rating factor, but not as strong as in UK. 2. Geodemographic type not significant for UMR data.

3. Copies of papers available from Stephen (in English, sorry!) References MADRIGAL ET AL 2009 What longevity predictors should be allowed for when valuing pension-scheme liabilities?, British Actuarial Journal (to appear). RICHARDS, S. J. AND JONES, G. L. 2004 Financial aspects of longevity risk, SIAS. RICHARDS, S. J. 2008 Applying survival models to pensioner mortality data, British Actuarial Journal, Vol 14, Part II, No. 61.

RICHARDS, S. J. 2010 A handbook of parametric survival models for actuarial use , Scandinavian Actuarial Journal (to appear).

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